Computability and complexity in analysis

Proof Mining in Analysis: Computability and Complexity

Proof Mining consists in extracting from prima facie non-constructive proofs constructive information. For that purpose many techniques mostly based on negative translation, realizability, functional interpretation, A-translation and combinations thereof have been developed. After introducing various different approaches to Proof Mining we present an application of ‘monotone functional interpre...

Computability and Complexity

ion Abstraktion Acceptance problem Akzeptanz-Problem Accepted akzeptiert Accepting state akzeptierender Zustand Ackermann function Ackermann-Funktion Algorithm Algorithmus Alphabet Alphabet Ambiguity problem Zweideutigkeitsproblem Amortized analysis amortisierte Analyse Application Anwendung Argument (Funktions-)Argument Automaton (endlicher) Automat Automaton language (L(M)) die Sprache eines ...

Honest Computability and Complexity

Computations manipulate representations of objects, most often strings of symbols taken from some finite alphabet, rather than the objects themselves. Numbers, for example, are usually denoted by sequences of decimal, or binary, or unary digits. In logic, one therefore distinguishes between numbers n, which reside in an ideal Platonic world, and numerals ⌜n⌝, their symbolic representation as (f...

Computability and Complexity

Dagstuhl - Seminar 99461 on Computability and Complexity in Analysis

Variants of Computable Analysis and Realizability Andrej Bauer Carnegie Mellon University, Pittsburgh, USA There are several schools of computable analysis, among others: recursive analysis, type II computability, effective domains, effective T0-spaces, effectively given continuous domains, effective equilogical spaces, and BlumSmale-Shub Real Numbers Machine. In this talk I show that all of th...